Predicting Capacity of Hard Carbon Anodes in Sodium-Ion Batteries
Using Porosity Measurements
Bommier, C., Luo, W., Gao, W. Y., Greaney, A., Ma, S., & Ji, X. (2014). Predicting
capacity of hard carbon anodes in sodium-ion batteries using porosity
measurements. Carbon, 76, 165-174. doi:10.1016/j.carbon.2014.04.064
10.1016/j.carbon.2014.04.064
Elsevier
Accepted Manuscript
http://cdss.library.oregonstate.edu/sa-termsofuse
Predicting Capacity of Hard Carbon Anodes in Sodium-Ion Batteries Using Porosity
Measurements
Clement Bommier1, Wei Luo1, Wen-Yang Gao3, Alex Greaney2, Shengqian Ma3 and Xiulei Ji1
1. Department of Chemistry, Oregon State University, Corvallis, Oregon, 97331, USA
2. Department of Mechanical, Industrial and Materials Engineering, Oregon State
University, Corvallis, Oregon, 97331, USA
3. Department of Chemistry, University of South Florida, Tampa, Florida, 33620, USA
Abstract
We report an inverse relationship between measurable porosity values and reversible capacity
from sucrose-derived hard carbon as an anode for sodium-ion batteries (SIBs). Materials with
low measureable pore volumes and surface areas obtained through N2 sorption yield higher
reversible capacities. Conversely, increasing measurable porosity and specific surface area
leads to sharp decreases in reversible capacity. Utilizing a low porosity material, we thus are
able to obtain a reversible capacity of 335 mAh g-1. These findings suggest that sodium-ion
storage is highly dependent on the absence of pores detectable through N2 sorption in sucrosederived carbon.

Corresponding author: Tel: +1 541-737-6798, E-mail: david.ji@oregonstate.edu
1
1. Introduction
In the coming years, research and development of new energy technologies will be an
essential part of meeting rising electricity demand while offsetting growing environmental
concerns. There are two concurrent priorities in this effort: a drive towards renewable energy
generation combined with an inexpensive and large-scale electricity energy storage (EES).
The state-of-the-art EES system currently available is lithium-ion batteries (LIBs). [1] Though
they offer high reversibility and efficiency, they are also very expensive due to the rarity and
high extraction costs of lithium metal. This is where sodium-ion batteries (SIBs) present
themselves as a feasible alternative.[2] They share many similar properties with LIBs, but are
much more economically advantageous due to the low cost of sodium, as it is the 6th most
abundant element in Earth’s crust and can easily be mined from abundant sources. This
renders it 95% cheaper than Lithium. [3]
However, the size difference between the two ions, 95 pm for Na+ versus 68 pm for Li+,
makes it such that the technologies of LIBs and SIBs are not always interchangeable. This is
especially true when considering the anode material. Unlike LIBs, SIBs cannot use graphitic
materials for anodes. It has been well documented that intercalation of Na+ in graphite is
unfavorable.[4,5] Whereas in the rocking-chair model of LIBs, the graphitic anode possesses
the chemical formula of LiC6 after intercalation, its SIB counterpart has a chemical formula of
NaC70.[6] This has led to significant efforts aimed towards developing a suitable SIB anode. A
variety of options have been explored, including carbon materials,[7,8,9,10] phosphorous,[11,12]
organic
compounds,[13]
metal
oxides,[14,15,16]
metal
nitrides,[17]
sodium
ternary
compounds,[18,19,20,21,22] thin film anodes[23] as well as various types of alloys.[24,25,26,27,28,29,30]
Of the above candidates, carbon-based materials have distinguished themselves as a
promising solution as they are cheap, easily attainable and non-toxic. Various types have been
investigated such as carbon black,[31] carbon microspheres,[32] hierarchically porous carbon,[33]
nitrogen-doped carbons[34,35] graphene nanocomposites[36] and nanostructures.[37,38] While all
2
these materials have their various merits, much interest still remains in the research disordered
graphitic carbon—otherwise known as hard carbon.
In previous studies, hard carbon has demonstrated a stable cycling capacity of 285
mAh g-1 and 300 mAh g-1 by Alcántra et al.[31] and Dahn et al.[10], respectively, and has lately
managed to surpass 300 mAh g-1 for over 100 cycles as reported by Palacin et al.[39] The
widely-accepted theory suggests that hard carbon can effectively store sodium ions in the
nanopores that stem from its randomly scattered graphene nanodomains — this is otherwise
known as the ‘falling-card’ model.[9] This concept leads us to investigate whether a greater
nanoporosity will be more effective for sodium-ion storage, which would thus result in a
higher reversible capacity.
Herein, we demonstrate a model that strongly suggests reversible capacity of SIBs is
inversely proportional to increases in both pore volume and surface area of the hard carbon
active material. By reducing the measurable porosity, we report one of the highest reversible
capacities to date of hard carbon at 335 mAh g-1.
2. Experimental Section
2.1. Materials Synthesis and Characterizations
The active hard carbon material used in this study is derived from sucrose (Macron
Chemicals). Sucrose is dehydrated for 24 hrs under atmospheric conditions at 180 ºC. Chunks
of the resulting material are pyrolysed under continuous argon gas flow in a tube furnace for 6
hrs. The pyrolysis was done at 800 ºC, 900 ºC, 1000 ºC and 1100 ºC, with a heating rate of 5
ºC min-1. CO2 activation was performed on samples pyrolysed at 1000 ºC at temperatures of
700 ºC, 800 ºC and 900 ºC for durations of 1 hr, 2 hrs, 5 hrs and 10 hrs with a heating rate of
10 ºC min-1 and a CO2 flow rate of 100 cm3 min-1. Following the synthesis of the hard carbon
material, it was characterized with X-ray diffraction (XRD) using a Rigaku Ultima IV
Diffractometer operating at 40 kV and 40 mA using Cu Kα radiation (λ = 1.5406 Å) and a
3
WITec confocal Raman Spectroscopy with a 514 nm laser. Surface morphology was obtained
through a FEI Quanta 600 SEM. Surface area was obtained through the Brunnauer-EmmettTeller model (BET) and pore volume was obtained through Density Functional Theory (DTF)
using N2 sorption with a Micromeritics ASAP 2020 Surface Area Analyzer. Elemental
analyses were performed on the samples pyrolysed at different temperatures by the
Environmental Division of ALS Global.
2.2. Electrochemical Measurements
Electrodes were made using a 7:2:1 weight ratio of hard carbon, Super-P carbon black
(TimCal) and poly-1,1-difluoroethene (PVDF) binder, respectively. This was mixed in an nmethyl-2-pyrrodilinone (NMP) solvent before being doctor-bladed onto copper foil. Once the
anodes were prepared they were punched into disks with loading masses typically between
1.5 to 1.8 mg cm-2 which were then vacuumed and moved into in an argon-filled glove box
for coin cell assembly. The coin cells were composed of a solid sodium metal counter
electrode, a glass-fiber separator (PALL) and a 1.0 M NaClO4 electrolyte solution dissolved
in a 1:1 weight mixture of ethylene carbonate / propylene carbonate (EC/PC). The batteries
were galvanostatically cycled on an Arbin BT2000 system at an initial current rate of 40 mA
g-1, which translates into a cycling rate of C/8 as we consider 300 mAh g-1 to be 1 C. Higher
rates from 100 mA g-1 to 1 A g-1 were used to investigate the rate capability of the materials.
At a current rate of 40 mA g-1 carbon black has a reversible capacity of 150 mAh g-1, which is
included in the supplementary section (Figure S1). Since our electrodes comprise 20 weight%
of carbon black, this would represent a capacity contribution of 30 mAh g-1. Being on the side
of caution, we removed 40 mAh g-1 of capacity at a current rate of 40 mA g-1, which gives us
the reversible capacity of 335 mAh g-1.
4
Cyclic voltammetry was performed on a VMP-3 multi-channel workstation at a scanning rate
of 0.2 mV s-1 at room temperature. Statistical modeling data was obtained through the R
programming package.
3. Results and Discussion
We pyrolysed sucrose at 1000 ºC for preparation of the hard carbon. We first tested whether
increasing porosity via CO2 activation would lead to higher capacities. The CO2 activation
can be described by the following reaction:
Table 1. Measurable pore volume/surface area data and capacities for samples obtained
through CO2 activation.
CO2 Activation
Temperature/
Time
untreated
untreated
900 ºC-1hr
900 ºC-1hr
900 ºC-2hrs
900 ºC-2hrs
900 ºC-5hrs
900 ºC-5hrs
900 ºC-10hrs
900 ºC-10hrs
800 ºC-1hr
800 ºC-1hr
800 ºC-2hrs
800 ºC-2hrs
800 ºC-5hrs
800 ºC-5hrs
800 ºC-10hrs
800 ºC-10hrs
700 ºC-1hr
700 ºC-1hr
700 ºC-2hrs
700 ºC-2hrs
700 ºC-5hrs
700 ºC-5hrs
700 ºC-10hrs
700 ºC-10hrs
DFT Pore
Volume (cm3 g-1)
BET Surface
Area
(m2 g-1)
abs(ln
DFT Pore
Volume)
ln
Surface
Area
1st cycle
Reversible
Capacity
(mAh g-1)
0.042
0.042
0.177
0.177
0.265
0.265
0.607
0.607
0.908
0.908
0.082
0.082
0.126
0.126
0.123
0.123
0.197
0.197
0.122
0.122
0.094
0.094
0.099
0.099
0.140
0.140
58.7
58.7
219.6
219.6
340.6
340.6
832.5
832.5
1410.3
1410.3
102.6
102.6
154.4
154.4
155.4
155.4
256.9
256.9
152.1
152.1
126.4
126.4
141.9
141.9
196.5
196.5
3.16
3.16
1.73
1.73
1.33
1.33
0.50
0.50
0.10
0.10
2.51
2.51
2.07
2.07
2.09
2.09
1.62
1.62
2.10
2.10
2.37
2.37
2.31
2.31
1.97
1.97
4.07
4.07
5.39
5.39
5.83
5.83
6.72
6.72
7.25
7.25
4.63
4.63
5.04
5.04
5.05
5.05
5.55
5.55
5.02
5.02
4.84
4.84
4.95
4.95
5.28
5.28
282.9
290.4
239.3
214.9
208
186.5
107.1
120.7
49.3
43.6
257.4
229.6
240.6
236.6
221.7
218.5
268.3
228.9
232.5
225.3
205.8
192.7
263.5
255.1
249.8
241.5
5
Irreversible
Capacity
(%)
28.6%
21.0%
33.5%
22.2%
45.0%
54.9%
71.9%
75.7%
80.8%
89.9%
29.1%
32.9%
31.2%
32.0
23.9%
44.0%
28.9%
37.0%
25.6%
34.3%
32.7%
45.8%
21.4%
29.5%
25.1%
25.3%
This reaction consumes part of the solid carbon, thereby increasing its porosity and surface
area. Samples were initially activated at a temperature of 900 ºC, with reaction durations of 1
hr, 2 hrs, 5 hrs and 10 hrs (Table 1). Half cells were then made from the activated carbons and
characterized by galvanostatic charge/discharge cycling (Figure 1a). The capacities reported
are those obtained during the desodiation process of the anode, often referred to as reversible
capacity, and are solely attributed to the sucrose-derived hard carbon. An activated sample is
referred to as ‘T ºC-n hrs’ if it was treated at T ºC for n hours.
Figure 1. Initial cycling performance at 40 mA g-1 for carbons activated a) 900 ºC b) 800 ºC
c) 700 ºC for differernt durations and d) Initial cycling performance of carbons pyrolysed at
different temperatures.
The unactivated sample has an initial reversible capacity of 290 mAh g-1. After
activation of 1 hr and 2 hrs, the capacities drop to 239 mAh g-1 and 208 mAh g-1, respectively.
The samples that were activated for 5 hrs and 10 hrs exhibit even lower reversible capacities
of 120 mAh g-1 and 49 mAh g-1, respectively. It is evident that CO2 activation at 900ºC
decreases reversible capacity, with longer activation durations yielding progressively worse
results. We hoped that milder activation temperatures of 700 ºC and 800 ºC would be more
6
conducive to forming the desired nanopores, and offer an improvement over those obtained at
900 ºC. However, these lower temperatures also caused a decrease in reversible capacity
(Figure 1b, c). Interestingly, longer activation durations at lower temperatures do not
necessarily lead to lower capacities. Contrary to what had been observed at 900 ºC, the 700
º
C-2 hrs activated carbon shows an initial reversible capacity of 206 mAh g-1, the lowest of
the 700 ºC series, while the 700 ºC-5 hrs has the highest reversible capacity at 264 mAh g-1.
We do not understand this phenomenon so far.
Figure 2. XRD patterns of different samples. a) Samples after CO2 activation at 900 ºC for
different durations. b) Samples of 700 ºC-10h and 800 ºC-10h. The untreated sample in a) and
b) is the hard carbon pyrolysed at 1000 ºC. c) Sucrose-derived hard carbon pyrolysed at
different temperatures, unactivated.
Seeing losses in capacity following CO2 activation led us to search for a link between
the physical properties of the materials and their sodium-ion storage performance. XRD
patterns and Raman spectra were collected for the untreated carbon and its CO2 activated
counterparts (Figure 2a,b and Figure S2). All the samples obtained demonstrate the typical
7
characteristics of amorphous carbon: broad peaks at 24º and 43º, representing the (002) and
(100) planes, respectively. The 900 ºC-5 hrs and 900 ºC-10 hrs samples exhibit even less
resolved XRD peaks, indicating a disruption of the amorphous structure by activation. Raman
spectra were inconclusive as well. The intensity ratios (Id/Ig) of the D-band (1350 cm-1)
representing the defected sp2 hybridized carbon over the G-band (1580 cm-1) measuring the
sp2 hybridized carbon show little variation (Table S1).An Id/Ig greater than 1 indicates a more
disordered carbon.
On the other hand, Density Functional Theory (DFT) pore volume and BrunauerEmmett-Teller (BET) surface area, calculated through N2 sorption measurements, show
dramatic changes following CO2 activation. All activated samples exhibit greater measurable
pore volume and surface area than the untreated control. The roughened surface morphology
is evident from the SEM images (Figure 3a,b). Higher CO2 activation temperatures and/or
longer reaction times give rise to larger pore volume and surface area. For example, the 900
º
C-10 hrs sample yields a surface area of 1410.3 m2 g-1 and a pore volume of 0.91 cm3 g-1,
comparing to a pore volume of 0.042 cm3 g-1 and a surface area of 58.7 m2 g-1 for the
unactivated material (Table 1).
Figure 3. SEM images showing that activation roughens surface morphology of sucrosederived carbon a) pyrolysed at 1000 ºC, unactivated, b) pyrolysed at 1000 ºC and activated
under CO2 at 900 ºC for 10 hrs. mesopores (2 nm-50 nm) and micropores (less than 2 nm) are
not observable at such low magnification.
8
(a)
(b)
Figure 4. Linear and natural logarithm transformed models plotting the reversible capacity in
the 1st cycle as a function of a) DFT specific pore volume b) BET specific surface area. The
best and worst results for the same materials were plotted.
We then plotted the first reversible capacity of all the samples as a function of their
measurable specific pore volume and surface area (Figure 4). When a linear regression
9
analysis was performed, the data yields coefficient of determination values (R2) of 0.889 for
the pore volume plot and of 0.879 for the surface area plot. To minimize the bias from the
outlying data points from 900 ºC-5hrs and 900 ºC-10hrs, while spreading out the clustered
ones, we performed a natural logarithm (ln) transform of the pore volume and surface area
values. As the pore volumes were quantities smaller than one for all samples, we further took
the absolute value (abs) to avoid negative numbers. The consequent R2 values obtained are
0.793 and 0.810 for the pore volume and surface area plots, respectively. Both models
demonstrate that reversible capacity is inversely proportional to DFT pore volume and surface
area.
Following the CO2 activation, we tried to gauge the effect that different sucrose pyrolysis
temperatures would have on the active material. For this, we utilized temperatures of 800 ºC,
900 ºC and 1100 ºC compared to the 1000 ºC used for our original material.
Once again, the reversible capacities are closely related to porosity values. The material
obtained at 1100 ºC has the lowest measurable pore volume and surface area, 0.015 cm3 g-1
and 24.8 m2 g-1, of the all samples obtained. It yields an initial reversible capacity of 335 mAh
g-1 with the contribution of super-P carbon taken out. Conversely, the sample pyrolysed at 800
º
C has the highest pore volume and surface area of the series at 0.199 cm3 g-1 and 265.8 m2 g-1,
respectively, and only achieved a reversible capacity of 200 mAh g-1 (Table 2).
When the data points from the different pyrolysis temperatures were added to the plots,
the R2 values stay relatively constant: 0.862 for the DFT Pore Volume model and 0.844 for
the Surface Area model. The R2 for the ln transformed models is also unchanged, standing at
0.786 for the ln DFT Pore Volume model and 0.816 for the ln Surface Area model (Figure 4).
Looking at the results of the regression analyses performed, all of the p-values obtained, with
30 degrees of freedom (DF), are below 1.5∙10-11. A p-value is the probability of obtaining a
test statistic (e.g. R2) equal to or greater than one obtained at random. A p-value of less than
10
0.05 is considered statistically significant. This proves that there is very strong evidence
linking reversible capacity to DFT Pore Volume and Surface Area (Figure S3).
Table 2- Measureable pore volume/surface area data and capacities for samples obtained at
different pyrolysis temperatures.
Pyrolysis
Temperature
800 ºC
800 ºC
900 ºC
900 ºC
1000 ºC
1000 ºC
1100 ºC
1100 ºC
DFT Pore Volume
(cm3 g-1)
BET Surface Area
(m2 g-1)
abs(ln DFT
Pore
Volume)
0.199
0.199
0.069
0.069
0.042
0.042
0.015
0.015
265.8
265.8
92.8
92.8
58.7
58.7
24.8
24.8
1.61
1.61
2.68
2.68
3.16
3.16
4.19
4.19
ln
Surface
Area
1st cycle
Reversible
Capacity
(mAh g-1)
5.58
5.58
4.53
4.53
4.07
4.07
3.21
3.21
199.8
221.4
260.9
248.2
282.9
290.4
335.0
299.0
Irreversible
Capacity
(%)
34.0%
23.4%
24.0%
14.3%
28.6%
21.0%
4.4%
20.3%
We are aware that it is possible that impurities in pyrolysed carbon can have an impact
on the Na+ ion storage. Elemental analyses for the carbons obtained at different pyrolysis
temperatures were conducted. All the materials tested have carbon ranging from 93 to 97
mass % and hydrogen from 0.2 to 0.6 mass % with the rest as oxygen (Table S2). Our data are
expected as it was reported that pyrolysis of cellulose, as a polymer of sucrose, occurs well
below 800 ºC with mainly carbon as the composition.[40] It is evident now the very much
different capacities from the materials pyrolysed at various temperatures were obtained at the
similar levels of extraneous hydrogen and oxygen residues. Such a vast capacity variations
can be only attributed to the porosity differences between these samples.
As was the case with the CO2 activation samples, the XRD profiles and Raman
spectroscopy data obtained from the samples pyrolysed at different temperatures varied little.
The XRD patterns all exhibit the (002) and (100) peaks, while the Id/Ig ratios obtained from
Raman spectra range narrowly from 0.97 to 1.04 (Figure 2c, Figure S2, and Table S1).
11
Figure 5. Reversible capacity vs. logit transform of the percentage of the unexposed carbon
atoms. The logit transform takes the formula of:
This allows for
a greater spread of percentage values on the x-axis.
Considering that N2 can only be adsorbed in pores approximately equal to or larger
than ~ 0.4 nm,[41] we can infer from the models that Na+-ion storage in hard carbon is highly
dependent on the absence of such open pores. This leads us to classify the carbon atoms that
contribute to the surface area and porosity as ‘exposed carbon atoms’. The percentage of
‘exposed carbon atoms’ is available through the equation
⁄
⁄
where At represents the measured BET surface area, and r is the radius of a carbon atoms; MM
and NA, are the Molar Mass and Avogadro’s number, respectively.
We assume that an exposed carbon atom contributes to measurable surface area with a single
hemisphere, whose area is equal to 2πr2 with r equal to 0.73 Å, the half of the bond length of
adjacent carbon atoms in the graphene sheet. We can estimate ratio between the exposed
carbon atoms in numerator and the total number of atoms in the denominator.
12
We then used this to calculate for the percentage of unexposed carbon atoms by using the
equation
Using this metric it was found that the material exhibiting the lowest reversible capacity had
only 8.7% of unexposed carbon atoms, while the best performing material had 98.4%
unexposed carbon atoms. Plotting the values of reversible capacity vs. Logit transform of the
percentage of the unexposed carbon atoms yields an R2 value of 0.89 with a p-value of 6.3∙1016
on 30 DF (Figure 5 & Figure S4). This suggests that, unlike unexposed atoms, exposed
carbon atoms have inferior contributions towards Na+-ion storage. This may be due to the fact
that the exposed carbon atoms tend to act as nucleation sites for solid electrolyte interphase
(SEI), a passivation layer that stems from the decomposition of the electrolyte solvents or
salts. This passivation layer may disable the Na+-ion storage on the electrode surface due to
its electronically-insulating nature and block the access of Na+ ions to the enclosed voids
inside the carbon structure.
Figure 6. A comparison of Nyquist plots of electrochemical impedance spectroscopy results
of high (1410 m2 g-1) and low (24 m2 g-1) surface area carbon materials as electrodes. The
measurements were taken ex-situ at various stages during the first discharge. The plots at the
same voltages from high-surface-area and low-surface-area electrodes have been
superimposed for clarity.
13
Evidence of the greater SEI formation on high surface area material can be seen through
a comparison of electrochemical impedance spectroscopy (EIS) measurements. These were
taken at various voltages in the course of the initial discharge. The low-surface-area carbon
(24 m2 g-1), referred to as lowSAC, has the larger initial semi-circle, indicating a higher
resistivity for interface charge transfer. However, once the batteries have been fully
discharged at 0.01 V, the high surface area carbon (1410 m2 g-1), referred to as highSAC,
exhibits a much larger semi-circle than the lowSAC (Figure 6). Further proof of the difference
in SEI formation is seen when comparing the 1st and 2nd cycle CV curves of highSAC and
lowSAC. Since the bulk of SEI formation occurs in the first cycle, the area enclosed by the
CV curve during the 2nd cycle is expected to drop as there will be a less significant formation
of the passivation layer. When comparing the enclosed areas, the highSAC showed a 26%
decrease of the enclosed area from the first to the second cycle, while the lowSAC only
showed a 6% decrease (Figure S5 & Table S4). Moreover, there is no oxidation peak in the
anodic scan associated to the sodium-metal oxidation with the highSAC, which indicates that,
besides the SEI formation, even the deposited sodium metal or ions in the nanopores of
highSAC are not electrochemically removable. This is partially responsible to the low
capacity of high surface materials. In summary, both the EIS and CV measurements support
that more SEI was formed with the high surface area material. Similar phenomenon has been
observed on higher-surface-area carbon materials in Li-ion batteries.[7]
14
Figure 7. Natural logarithm (ln) transformed models comparing irreversible capacity
percentage of the first cycle versus absolute value of ln pore volume and ln surface area. The
best and worst results for the same materials were ploted.
It is also well known that SEI formation causes irreversible capacity during the first
cycle and is proportional to the measurable surface area of carbon materials.[42,43] To confirm
this, we plotted the percentage of irreversible capacity over the discharge capacity in the first
cycle vs. the ln transformed pore volume and surface area for all the samples (Figure 7). A
linear regression analysis yields reasonable R2 values. Both corresponding p-values, obtained
with 30 DF, are below 7∙10-9, thereby implying that there is strong evidence linking
irreversible capacity with DFT Pore Volume and Surface Area (Figure S6).
We further investigated the electrochemical properties of the two materials. The
charge/discharge profiles differ greatly between lowSAC and highSAC. The former displays
two distinct features during desodiation. The first is a relatively flat plateau that runs from
0.05 to 0.2 V. This is followed by a sloping curve to 2.0 V. The flat plateau of the desodiation
curve can be attributed to the de-insertion of the sodium ions from voids between graphite
nanodomains. The sloping curve stems from the sodium-ion de-intercalation out of graphite
15
nanocrystals. The latter eschews these characteristics. Instead it exhibits a capacitor-like
behavior where the voltage rises almost linearly from 0.01 V to 2.0 V during the same
desodiation process (Figure 8a, b).[9]
(b)
(a)
Figure 8. a) Galvanostatic charge-discharge profiles of lowSAC, carbon pyrolysed at 1100 ºC,
unactivated, b) charge-discharge profiles of highSAC, carbon pyrolysed at 1000 ºC and
activated at 900 ºC for 10 hrs.
The lower reversible capacity for high surface area materials is clearly associated with
the loss of capacity obtained below ~ 0.2 V. This portion of capacity can be attributed to the
de-insertion of Na+ ions from voids inside the closed hard carbon structure according to the
hypothesis by Dahn et al.
[6,9]
. With higher porosity generated, such closed hard carbon
structure has been destroyed, which is responsible for the observed loss of capacity at low
voltage, e.g. below 0.2 V. The capacity obtained at higher than 0.2 V may be from either the
de-intercalation of ions from graphitic structures or electrical double layer capacitance. [9,44] In
order to quantify the loss of capacity at low voltages, a ratio of the reversible capacity under
0.2 V over the total reversible capacity was calculated (Table S5).
16
When comparing these ratios to the respective measurable specific surface areas, we
discovered that low surface area materials typically obtain around 50% of their reversible
capacity below 0.2 V. On the other hand, higher surface area materials, notably the 900 °C5hrs and 900 °C-10hrs samples, obtain only ~10% of their reversible capacity under 0.2 V.
The aforementioned ratio vs. surface area was plotted and fitted with a linear regression
model that yields an R2 value of 0.831 and a p-value of 4.2∙10-13 (Figure S7). When increasing
open porosity of hard carbon, the volume of the closed hard carbon structure conducive for
Na+ storage is certainly diminished. This is why the capacity is inversely proportional to the
specific pore volume/surface area.
Cyclic voltammetry (CV) was conducted at a scanning rate of 0.2 mV s-1 for lowSAC.
During the initial cathodic scan, there is a broad reduction plateau between 0.2 to 0.6 V,
indicative of SEI formation. The CV curves have sharp reduction and oxidation peaks
between 0.01 V to 0.2 V. The reduction peak is attributed to insertion of Na+ into the voids in
hard carbon, while the oxidation peak signifies their removal (Figure 9a).[45] These results
agree well with the charge/discharge profiles, as the charge and discharge curve plateau when
the voltage is below 0.2 V. CV was also conducted on the highSAC, but it was found that the
oxidation peak associated to sodium-metal oxiation in the anodic scan occurring between 0.01
and 0.2 V had mostly vanished (Figure S5). Instead, the CV curve for the high surface area
material begins to adopt the characteristics of a capacitor. This corroborates what was seen in
the charge/discharge curves as well as the observation that increased surface area and porosity
lead to a decrease of Na+ ion storage features, which leads to the loss of reversible capacity
obtained at voltages below 0.2 V.
17
Figure 9. Electrochemical characterizations of C-1100. a) CV curves for the first three cycles
at a scanning rate of 0.2 mV s-1, b) galvanostatic cycling at different current rates , c) long
term galvanostatic cycling at a high rate of 300 mA g-1.
We also investigated the cycling performance of the C-1100 with different current rates
(Figure 9b). Decreases in specific capacity are observed at higher currents, though this is
expected due to the kinetic limitation of hard carbon. After 100 cycles, the carbon material
showed almost no loss in capacity at 40 mA g-1 when compared to the capacities of the initial
18
cycles. A long term cycling at 300 mA g-1 was also conducted, and after 500 cycles, 70% of
the initial capacity remained (Figure 9c).
4.
Conclusion
We demonstrate that there is an inherent relationship between the porosity and reversible
capacity: increases of measurable porosity are very strongly associated with lower reversible
capacities. This insight may be applied to other bio-mass converted hard carbons as anodes in
SIBs, as it reveals that superior Na+ ion storage in such batteries is dependent on the absence
of pores detectable through N2 sorption. Using a low measurable surface area/porosity hard
carbon we are able to achieve a reversible capacity of 335 mAh g-1 at a current rate of 40 mA
g-1 along with a relatively stable long term cycling (500 cycles) at 300 mA g-1. In our
laboratories, there are ongoing efforts in search of yet lower pore volumes aimed for further
increasing reversible capacity while lowering irreversible capacity.
5. Acknowledgements
X. J. gratefully acknowledges the financial support from Advanced Research Projects
Agency-Energy (ARPA-E), Department of Energy of the United States, Award Number: DEAR0000297TDD. We thank Dr. Jong-Jan Lee, Dr. Yuhao Lu, Dr. Sean Vail and Dr. Long
Wang from Sharp Labs America for their suggestions and assistance. The authors would like
to thank Dr. Peter Eschbach and Ms. Teresa Sawyer for the SEM measurements in OSU EM
Facility funded by National Science Foundation, the Murdock Charitable Trust and the
Oregon Nanoscience and Microtechnology Institute. We appreciate Professor Chih-Hung
Chang and Mr. Changqing Pan for Raman spectra studies. Lastly, we are grateful to Professor
Michael M. Lerner for his advice.
19
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24
Supporting Information
Predicting Capacity of Hard Carbon Anodes in Sodium-Ion Batteries Using Porosity
Measurements
Clement Bommier1, Wei Luo1, Wen-Yang Gao3, Alex Greaney2, Shengqian Ma3 and Xiulei Ji1
1. Department of Chemistry, Oregon State University, Corvallis, Oregon, 97331, USA
2. Department of Mechanical, Industrial and Materials Engineering, Oregon State
University, Corvallis, Oregon, 97331, USA
3. Department of Chemistry, University of South Florida, Tampa, Florida, 33620, USA

Corresponding author: Tel: +1 541-737-6798, E-mail: david.ji@oregonstate.edu
25
+
Potential (V vs. Na/Na )
2.0
1.5
1.0
0.5
0.0
0
1
Specific Capacity (mAh g )
300
250
(b)
Super P
(a)
30
60
100
200
300
400
-1
Specific Capacity (mAh g )
120
300 600 1200 600 300 120
60
30
-1
mA g
200
150
100
50
0
0
5
10
15
20
25 30 35 40
Cycle Number
45
50
55
60
Figure S1. Electrochemical performance of Super-P, a) Galvanostatic first cycle
charge/discharge profiles, b) cycling performance at different rates.
26
Figure S2. Raman Spectra shifts for a) 900 ºC CO2 activation series b) 700 ºC -10hrs and
800 ºC-10hrs CO2 activation c) Different Pyrolysis temperatures. The untreated label refers to
the sucrose sample pyrolysed at 1100 ºC. The peak at 1350 cm-1 is from the disordered carbon,
while the peak at 1580 cm-1 is from the graphitic carbon.
27
(b)
(a)
Residual standard error: 24.03 on
30 degrees of freedom
Multiple R-squared: 0.8625,
Adjusted R-squared: 0.8579
F-statistic: 188.2 on 1 and 30 DF
p-value: 1.842e-14
Residual standard error: 29.98 on 30
degrees of freedom
Multiple R-squared:0.7859
Adjusted R-squared: 0.7788
F-statistic: 110.1 on 1 and 30 DF
p-value: 1.468e-11
(d)
(c)
Residual standard error: 27.54 on
30 degrees of freedom
Multiple R-squared: 0.8194
Adjusted R-squared:0.8133
F-statistic: 136.1 on 1 and 30 DF
p-value: 1.127e-12
Residual standard error: 26.56 on
30 degrees of freedom
Multiple R-squared: 0.8319
Adjusted R-squared: 0.8263
F-statistic: 148.5 on 1 and 30 DF
p-value: 3.792e-13
Figure S3. Linear regression models of a) Reversible capacity vs. measurable DFT pore
volume b) Reversible capacity vs. ln transformed DFT pore volume c) Reversible capacity vs.
measurable surface area d) Reversible capacity vs. ln transformed surface area.
28
Residual standard error: 21.48 on
30 degrees of freedom
Multiple R-squared: 0.8901,
Adjusted R-squared: 0.8865
F-statistic: 243 on 1 and 30 DF,
p-value: 6.268e-16
Figure S4. Linear regression model of reversible capacity vs. logit transform of percentage of
the unexposed carbon atoms. The logit transform is obtained through
29
(a)
(b)
Figure S5. CV curves of (a) lowSAC, (b) highSAC. Scanning rate: 0.2 mV/s
30
(a)
(b)
Residual standard error: 0.1119 on
30 degrees of freedom
Multiple R-squared: 0.681,
Adjusted R-squared: 0.6703
F-statistic: 64.03 on 1 and 30 DF
p-value: 6.233e-09
Residual standard error: 0.108 on
30 degrees of freedom
Multiple R-squared: 0.7031,
Adjusted R-squared: 0.6932
F-statistic: 71.05 on 1 and 30 DF
p-value: 2.087e-09
Figure S6. Linear regression models of a) Irreversible capacity vs. ln transformed DFT pore
volume b) Irreversible capacity vs. ln transformed surface area.
31
2
Incremental Surface Area (m )
80
60
900 C-1h
40
20
0
0
50
100
Pore Size (Å)
150
2
400
Incremental Surface Area (m )
2
Incremental Surface Area (m )
2
Incremental Surface Area (m )
(a)
300
900 C-5h
200
100
0
0
50
100
Pore Size (Å)
150
300
250
200
900 C-2h
150
100
50
0
0
50
100
Pore Size (Å)
150
600
500
400
900 C-10h
300
200
100
0
0
50
100
Pore Size (Å)
150
2
Incremental Surface Area (m )
800 C-1h
20
15
10
5
0
0
50
100
Pore Size (Å)
150
2
2
25
Incremental Surface Area (m )
10
2
Incremental Surface Area (m )
30
Incremental Surface Area (m )
(b)
8
800 C-5h
6
4
2
0
0
50
100
Pore Size (Å)
150
32
40
35
800 C-2h
30
25
20
15
10
5
0
0
50
100
Pore Size (Å)
150
40
35
30
800 C-10h
25
20
15
10
5
0
0
50
100
Pore Size (Å)
150
2
1
0
50
20
700 C-5h
15
10
5
0
5
0
0
50
100
Pore Size (Å)
150
1100 C
0.4
0.3
0.2
0.1
0.0
50
100
Pore Size (Å)
150
1.2
1.0
900 C
0.8
0.6
0.4
0.2
0.0
-0.2
0
50
100
Pore Size (Å)
150
150
8
700 C-10h
6
4
2
0
0
0.6
50
2
0
50
100
Pore Size (Å)
10
2
Incremental Surface Area (m )
Incremental Surface Area (m )
1.4
2
10
2
25
700 C-2h
15
150
30
0.5
2
100
20
Incremental Surface Area (m )
0
0
(d
)
Incremental Surface Area (m )
700 C-1h
2
-1
25
Incremental Surface Area (m )
2
Incremental Surface Area (m )
2
Incremental Surface Area (m )
3
Incremental Surface Area (m )
(c)
50
100
Pore Size (Å)
150
0.5
0.4
1000 C
0.3
0.2
0.1
0.0
0
50
100
Pore Size (Å)
150
40
30
800 C
20
10
0
0
50
100
Pore Size (Å)
150
Figure S6. Pore size distribution (DFT model) calculated using 77 K N2 sorption data for a)
samples activated at 900 °C b) samples activated at 800 °C c) samples activated at 700 °C d)
Samples prepared at differing pyrolysis temperatures. Before CO2 activation, the carbon
sample was originally pyrolysed at 1000°C.
33
Residual standard error: 0.05634 on
30 degrees of freedom
Multiple R-squared:0.8307
Adjusted R-squared: 0.825
F-statistic: 147.2 on 1 and 30 DF
p-value: 4.243e-13
Figure S7. The ratio of capacity obtained below 0.2 V over the total reversible capacity as a
function of measurable specific surface area.
34
Table S1. The table represents the calculated Id/Ig ratios obtained.
Active Material
900 ºC -1hr
900 ºC -2hrs
900 ºC -5hrs
900 ºC -10hrs
Id/Ig
1.028
1.021
1.039
1.042
Active Material
700 ºC -10hrs
800 ºC -10hrs
Id/Ig
0.974
1.003
Active Material
800 ºC
900 ºC
1000 ºC (untreated)
1100 ºC
Id/Ig
1.009
1.018
1.031
1.035
Table S2. Elemental analysis of hard carbons obtained at different pyrolysis temperatures.
Pyrolysis
Temperature
800 °C
900 °C
1000 °C
1100 °C
Carbon Mass %
Hydrogen Mass %
Oxygen Mass %
95.49
93.79
96.20
97.44
0.60
0.39
0.21
0.31
3.91
5.82
3.59
2.25
35
Table S3. Respective percentages of exposed and exposed carbon atoms. The logit transform
is obtained through the equation
. This was done to spread out
the clustered percentage values that were all above 90%.
Material
900 ºC-1hr
900 ºC-2hrs
900 ºC-5hrs
900 ºC-10hrs
800 ºC-1hr
800 ºC-2hrs
800 ºC-5hrs
800 ºC-10hrs
700 ºC-1hr
700 ºC-2hrs
700 ºC-5hrs
700 ºC-10hrs
800 ºC
900 ºC
1000 ºC
1100 ºC
% Exposed
Carbon
atoms
14.2%
22.0%
53.9%
91.3%
6.6%
10.0%
10.1%
16.6%
9.8%
8.2%
9.2%
12.7%
17.2%
6.0%
3.8%
1.6%
%
Unexposed
Carbon
atoms
85.8%
78.0%
46.1%
8.7%
93.4%
90.0%
89.9%
83.4%
90.2%
91.8%
90.8%
87.3%
82.8%
94.0%
96.2%
98.4%
logit(unexposed
Carbon atoms)
1.80
1.26
-0.16
-2.35
2.64
2.20
2.19
1.61
2.21
2.42
2.29
1.93
1.57
2.75
3.23
4.12
Table S4. Calculated areas enclosed in the 1st and 2nd cycle CV curves for low surface area
carbon, lowSAC, and high surface area carbon, highSAC.
Material
lowSAC
highSAC
Area of
1st Cycle
0.373
0.249
36
Area of
2nd
Cycle
0.351
0.184
Percentage
drop
6.1%
26.1%
Table S5. Ratio of capacities obtained under 0.2 V over the total reversible capacity obtained.
The ratios are expressed in % values. The best and worst results for the same materials are
shown here.
Reversible
Capacity
(mAh g-1)
Capacity
Under 0.2
V (mAh g1
)
Capacity
% under
0.2 V
900 ºC-1hr
239.3
122.6
51.2%
900 ºC-1hr
214.9
114.8
900 ºC-2hrs
208.0
900 ºC-2hrs
900 ºC-5hrs
Material
Reversible
Capacity
(mAh g-1)
Capacity
Under 0.2
V (mAh
g-1)
Capacity
% under
0.2 V
800 ºC-1hr
257.4
141.7
55.0%
53.4%
800 ºC-1hr
229.6
124.5
54.2%
101.6
48.8%
800 ºC-2hrs
240.6
140.3
58.3%
186.5
86.2
46.2%
800 ºC-2hrs
236.6
132.6
56.0%
107.0
14.3
13.3%
800 ºC-5hrs
218.5
103.9
47.6%
800 ºC-5hrs
221.7
104.1
46.9%
Material
900 ºC-5hrs
120.7
20.5
17.0%
900 ºC-10hrs
49.3
6.7
13.6%
800 ºC-10hrs
268.3
158.9
59.2%
900 ºC-10hrs
43.6
4.5
10.4%
800 ºC-10hrs
228.9
126.2
55.1%
Material
Reversible
Capacity
(mAh g-1)
Capacity
Under 0.2
V (mAh g1
)
Capacity
% under
0.2 V
Material
Reversible
Capacity
(mAh g-1)
Capacity
Under 0.2
V (mAh
g-1)
Capacity
% under
0.2 V
700 ºC-1hr
232.5
122.7
52.8%
800 ºC
199.8
80.0
40.0%
700 ºC-1hr
225.3
117.1
52.0%
800 ºC
221.4
108.7
49.1%
700 ºC-2hrs
205.8
108.7
52.8%
900 ºC
260.9
142.2
54.5%
700 ºC-2hrs
192.7
96.9
50.3%
900 ºC
248.2
108.5
43.7%
700 ºC-5hrs
263.5
134.3
51.0%
1000 ºC
282.8
149.6
52.9%
1000 ºC
290.4
156.3
53.8%
700 ºC-5hrs
255.1
128.0
50.2%
700 ºC-10hrs
249.8
130.8
52.3%
1100 ºC
335.0
160.8
48.0%
700 ºC-10hrs
241.5
129.0
53.4%
1100 ºC
299.0
173.8
58.1%
37